Contingent transcranialists claim that the physical mechanisms of mind are not exclusively intracranial and that genuine cognitive systems can extend into cognizers' physical and socio-cultural environments. They further claim that extended cognitive systems must include the deep functional integration of external environmental resources with internal neural resources. They have found it difficult, however, to explicate the precise nature of such deep functional integration and provide compelling examples of it. Contingent intracranialists deny that extracranial resources can be components of genuine extended cognitive systems. They claim that transcranialists fallaciously conflate coupling with constitution and construe cognition as extending always from brains into world rather than world into brains. By using insights from recent research in developmental psychology and by explicating the nature of one form that deep functional integration can take, I argue that (i) transcranialists do not fallaciously conflate coupling wth constitution, and (ii) human emotional ontogenesis is a world-to-brain transcranial achievement.
I don't have the article yet, but I'm going to speculate that by "contingent intracranialists" Greenwood includes Adams and Aizawa. But, if so, we do not deny that extracranial resources can be components of genuine extended cognitive systems. We think that extracranial resources can be component of genuine extended cognitive systems, it's just that they are not. Here is the abstract to Adams and Aizawa, 2001:
Recent work in cognitive science has suggested that there are actual cases in which cognitive processes extend in the physical world beyond the bounds of the brain and the body. We argue that, while transcranial cognition may be both a logical and a nomological possibility, no case has been made for its current existence. In other words, we defend a form of contingent intracranialism
about the cognitive.